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Imperial Measures |
 By Ralph Ellis
Imperial Measurements, two words guaranteed to produce a shudder of horror in all school children. Nobody fully understands the system and it beggars belief that anyone would want to create such an unwieldy system in the first place - so how has it managed to last so long?
This is actually a serious question â exactly why was this complex system of measures invented? Does anyone really know? From the British perspective, the system seemed quite natural; having 14 pounds to the stone and 12 pence to the shilling were just part of the initiation into the culture, no more peculiar than having milk delivered to the doorstep.
To the rest of the world, however, it would seem that the figures of 1,760 yards to the mile and 51/2 yards to the rod were plucked out of thin air.
For who, in their right mind, would create a system of units that used fractions? Indeed, this mismatch of odd numbered units in the Imperial System has caused many eminent heads to be scratched over the years. No less an authority than Professor R. Connor, who has been working on weight and measures for more than forty years, says of the Imperial system of measures:
If we look again at the table of length, we might agree that the relation of inches to feet and feet to yard are not unreasonable, nor is that of the relation of rods to furlong to mile, but the entry â51/2 yards = 1 rodâ strikes a discordant note. For who in his right mind would establish a table of relationships using fractional parts? ... it can be taken for granted that the table was not set up âde novoâ (as new), but that two or more systems were being fused together to meet the needs of the times.
This is all very logical: the foot and yard were part of one measurement system and the furlong and rod were part of another. Where they met formed that uncomfortable 51/2 yards to the rod. But this does not exactly explain all the other odd ratios in the system, for instance, the 8 furlongs to the mile, the 320 rods to the mile and the 1,760 yards to the mile. They seem to be bizarre numbers; there has to be a simpler and more comprehensive solution to this problem than the fusion of two measurement systems.
That there may be some all-encompassing rationale to the system is borne out by some of its underlying symmetry, for even that rather odd sounding 51/2 yards to the rod still manages to work well throughout the system. The following are divisions of the Imperial System, expressed in yards and rods, yet both sides of the table are expressed in round numbers. One has to admit that the system does have an unexpected symmetry to it:
1760 yards (1 mile) divided by 5.5 = 320 rods,
220 yards (1 furlong) divided by 5.5 = 40 rods,
22 yards (1 chain) divided by 5.5 = 4 rods,
1 acre = 22 x 220 yds which is 4 x 40 rods.
The ease with which the 51/2 yard rod fits into the system has been recognised in the expert field as well. Professor Connor continues:
The pivot of the table of length, is the rod. It generates not only the furlong as a unit of length, but also the acre...
But this is a contradiction of the previous statement: the rod unit cannot be both the pivotal unit and also the accidental result of the fusion of two different systems. It would seem that the experts have come to no real conclusions beyond the âfactâ that the yard is a nice convenient household length and that a mishmash of units has grown up around it. For a long time I found this deeply unsatisfactory and I determined to find a better solution.
At last, after much patient study of the ancient texts, there does seem to be an alternative and very attractive solution to this age-old conundrum. Additionally, it is an answer that is relatively simple, which, according to the premise known as Occamâs razor, is always the test of a good theory.
Pi units
The solution I am proposing is that the whole table of units was based on the mathematical constant Pi. It is this use of Pi as a base structure to the Imperial Measurement System that has determined its peculiar nature and has also determined the length of that awkward 51/2âyard rod. Pi is not a nice round decimal number and therefore does not lend itself easily to subdivisions. It is also a fixed constant of nature, so there is not much that can done about that - the value of Pi cannot be changed, it just has to be circumvented. So if a designer wished to encompass the value of Pi into a building or, indeed, into a measurement system, the obvious solution would be to choose an approximation of Pi that was divisible by even units. A fraction of 22 : 7 springs to mind as an obvious choice, as it is a very simple approximation of the precise Pi number and it also has an even numbered numerator - the number 22.
My proposal is that the Pi ratio used in all of the Imperial System was 22 : 7. The numerator in this ratio, the number 22, is fundamental to the way in which the system was designed - it is the the base unit. Thus when looking at the Imperial system, it can be seen that there are 22 yards in a chain. Multiply this by ten and we find that the furlong is 220 yards. Finally, when going down the scale, if the number 22 is divided by 4 it produces the rather odd looking rod length of 51/2 units.
It would appear that there is a very simple solution to the peculiarities of the Imperial Measurement System; and that awkward 51/2 yard rod is simply a necessary by-product of our starting point of Pi. For Pi-based measurements to work out in even units, we have to use a multiple of 5.5 somewhere in the measurement system. The British Imperial Measurement System was not, therefore, just plucked out of thin air, it was a system based on Pi.
But if this is so, the implications are manifold and quite interesting, for it is indicating that the knowledge of the fractional approximation of Pi was known long ago. If this is so, the important question then comes - how long ago was this fraction of Pi known? How old is the Imperial measurement System? Some further investigation may provide an answer.
Pi Mile
Having found the symmetry of the sub-units of this measurement system, it is time to look at the mile length. When making this wonderfully new set of measurements, based on Pi, why would someone want to make them have such an awkward end-point; why derive the peculiar mile length of 1,760 yards? Where did this peculiar length come from? Well, as one might expect, this is another result of using Pi-based units; the result of using the 5.5 unit rod that is so central to this system.
The number 1760 is another Pi based number, a multiple of the Pi numerator of 22 units. Multiply 22 by 80 and we find that the mile is 1760 yards. Therefore any of the other sub-units in the system (which are based on the number 22, as in the table above) will happily divide into the mile length, including that awkward 5.5 yard rod. The result being that there are 320 rods, or 80 chains, or 8 furlongs to the mile.
This just has to be the most logical reason yet given for the mile length in the British Imperial Measures. Someone back in the dim and distant past knew of the fractional value of Pi and decided to encapsulate this into a new measurement system, one that has endured over the millennia into the present era. But the question still remains as to how and why was that done? How old is our Imperial Measurement system?
What follows may seem a little esoteric to some within the scientific community, but the artifacts are out there for anyone to witness and measure. One may disagree with the final interpretations that are made in the book âThoth, Architect of the Universeâ, but nevertheless facts are facts and there is an underlying simplicity to what follows. Why the caution at this point in this thesis? Well, put simply, the Imperial Measurement System was quite possibly derived from the construction of the Great Pyramid of Giza in Egypt!.
Now that may seem like a bold statement to make, but there are some good reasons for doing so. Firstly, like the Imperial Measurements themselves, the dimensions of the Great Pyramid are based on the function of Pi. In numerical terms, the height of this pyramid is a representation of the radius of a circle, and the circumference is a representation of the circleâs circumference. Thus, if the Great Pyramid was 7 units high, then the perimeter would be 44 of those same units (7 : 44). But the formula for the circumference of a circle is 2 x Pi x r, and if we extract the number of 2 from this formula (divide the number 44 by 2), I think the Pi fraction of 7 : 22 can be clearly seen in the dimensions of the Great Pyramid.
Fig 1 Pyramid as representation of a circle
So the Great Pyramid and the Imperial Measures appear to have been based on the same mathematical function - Pi, but where does the Imperial Mile measurement fit into all this? Well it is obvious that the pyramid does not really measure 44 units around the base, and yet to simply state that it actually measures 921.36 meters or even 3022 Imperial feet around the base means absolutely nothing. It is axiomatic that the Egyptians were using cubits, not feet or meters, and so it is to cubits we should look when deriving the measurements of the pyramids. The precise unit the Egyptians used was derived by Sir Isaac Newton in the 17th century, in his small booklet entitled âDissertation upon the Sacred Cubit of the Jews and other nationsâ. He derived the length by noting that the Kingâs chamber in the Great Pyramid was constructed to have dimensions of 10 x 20 cubits, and the resulting cubit therefore has a length of 52.35 centimeters (20.6 inches). If we were to use this original cubit to measure the circumference of the Great Pyramid, we would discover, to our amazement, that it has a perimeter length of 1760 royal (or Thoth) cubits â exactly the same number of units as contained in the 1760 yard Imperial mile. The absolute length of the cubit and the yard are different, of course, but the numerical symmetry remains the same.
Many may claim that this is coincidence, many may also say that the Imperial Measurement System is simply a base 22 numeric system and nothing to do with Pi. I would disagree. Firstly, it has been long rumoured in mythology, that the measurements of the Great Pyramid were somehow special. That is why Sir Isaac Newton wrote his pamphlet in the first place, in which he ponders over the dimensions of the Great Pyramid at Giza and many other ancient monuments. It is perhaps a shame that the base of the pyramid was covered in rubble in those times and that the perimeter length he was using was considerably short of the true length, otherwise Newton would certainly have discovered the same coincidence.
Secondly it is a fact that the Great Pyramid not only has a perimeter length of 1760 cubits, but also a height of 280 cubits. Thus this stupendous edifice, designed and erected some say in the early Bronze Age, is, as stated above, simply a representation of the circle formula of; circumference = 2 p r. So the ratio chosen for the design of the Great Pyramid was simply a 40 times multiple of the fractional approximation of Pi,
22 x 40 = 880, 7 x 40 = 280, pyramid ratio = 880:280
The base of the Great Pyramid Pyramid is then multiplied by 2 (2 p r), 2 x 880 = 1,760.
Fig 2 Great Pyramid a 40 times copy of Pi.
It is for this reason that the number 40 features in so many of the biblical stories. The Kings and judges of the Old Testament invariably had a life-span or reign-length of forty years, while any deliberations or wanderings in the deserts are also said to be 40 years or days in length. These time-spans were not real, of course, but merely an indication of an initiation. I have sought to prove in many of my books that the majority of the biblical stories were actually derived from events in Egypt, and the number 40 that is repeatedly used in these accounts demonstrated âto those who had ears to hearâ, that the person concerned had been initiated into the mystery and mathematics of the Giza pyramids. Note that the multiple of 40 also found its way into the dimensions of the Imperial unit of the acre, as was shown earlier.
But does all of this in any way prove that the Imperial Measures were actually based upon the dimensions of the Great Pyramid? Well, in the book âK2, Quest of the Godsâ, I go on to demonstrate how most of the Imperial Measurement units are key elements of the Great Pyramidâs design, especially that peculiar 5.5 unit rod-length. It would seem unlikely to me that all of the ratios, units and lengths contained in the Great Pyramid just happened to be the same as are contained within the Imperial Measurement system, and so I strongly suspect that the Imperial Measures were originally Egyptian (it is the ratios that are original, not the absolute lengths, which were altered by the Romans and various acts of the English parliament).
Thus the Great Pyramid appears to be a mathematical and meteorological constant carved not only into the fabric of these ancient monuments, but also into the culture of the Anglo-Saxon peoples. These traditions have been propagated down though the millennia, primarily through masonic institution, and it is for this reason that there is such opposition to the metric system. Indeed, such is the opposition within America to the Metric System, that the framework of the measurement system that was used to construct the Great Pyramid, have now been taken into space â encapsulated within the design of the Shuttle.
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